Funkcja kwadratowa jej postacie :
f(x) = ax² + bx + c postać ogólna
f(x) = a× ( x - p )² + q postać kanonicza gdzie W= ( p , q ) są to współrzędne wierzchołka
f(x) = a × ( x - x₁ ) × ( x - x ₂ ) postać iloczynowa gdy Δ > 0
f(x) = a × ( x - x₀ )² postać iloczynowa gdy Δ = 0
[tex]zad.1\\\\y=x^{2} +2x-1\\a=1,~~b=2,~~c=-1\\\Delta = b^{2} -4ac\\\\\Delta=2^{2} -4\cdot 1\cdot (-1)=4+4=8\\\sqrt{\Delta} =\sqrt{8} =2\sqrt{2} \\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor ~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a}\\\\\\x_{1} =\dfrac{-2-2\sqrt{2} }{2}=-1-\sqrt{2} ~~\lor~~x_{2} =\dfrac{-2+2\sqrt{2} }{2}=-1+\sqrt{2}\\\\y=1\cdot (x-(-1-\sqrt{2} ))\cdot (x-(-1+\sqrt{2} ))=(x+1+\sqrt{2} )\cdot (x+1-\sqrt{2} )\\\\[/tex]
[tex]zad.2\\\\y=x^{2} -3x-2\\a=1,~~b=-3,~~c=-2\\\Delta = b^{2} -4ac\\\\\Delta=(-3)^{2} -4\cdot 1\cdot (-2)=9+8=17\\\sqrt{\Delta} =\sqrt{17} \\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor ~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a}\\\\\\x_{1} =\dfrac{3-\sqrt{17} }{2} ~~\lor~~x_{2} =\dfrac{3+\sqrt{17} }{2}\\\\y=1\cdot (x- \dfrac{3-\sqrt{17} }{2})\cdot (x- \dfrac{3+\sqrt{17} }{2})\\\\y= (x- \dfrac{3-\sqrt{17} }{2})\cdot (x- \dfrac{3+\sqrt{17} }{2})[/tex]
